= Locally closed subset
A subset $B$ of a <topological space> $X$ is locally closed if $B=U\cap F$ for an <open set> $U$ and a <closed set> $F$. Equivalently, $B$ is open in its <closure> $\overline B$, or $\overline B\setminus B$ is closed in $X$. For the equivalence, $B\subseteq F$ implies $\overline B\subseteq F$, so $B=U\cap\overline B$. Relative complementation proves the second condition implies the third. Conversely, if $C=\overline B\setminus B$ is closed, then $B=(X\setminus C)\cap\overline B$ is such an intersection.
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